The differential equation of 3y = sqrt[3]{x} | vedclass

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Question

(A) Given equation: $3y = x^{1/3} + c$Step $1$: Differentiate both sides with respect to $x$.$\frac{d}{dx}(3y) = \frac{d}{dx}(x^{1/3} + c)$Step $2$: A

Vedclass · Accepted Answer

$\frac{dy}{dx} = \frac{1}{9x^{2/3}}$

Vedclass · Answer

(A) Given equation: $3y = x^{1/3} + c$Step $1$: Differentiate both sides with respect to $x$.$\frac{d}{dx}(3y) = \frac{d}{dx}(x^{1/3} + c)$Step $2$: Apply the power rule $\frac{d}{dx}(x^n) = nx^{n-1}$.$3 \frac{dy}{dx} = \frac{1}{3} x^{(1/3 - 1)} + 0$$3 \frac{dy}{dx} = \frac{1}{3} x^{-2/3}$Step $3$: Solve for $\frac{dy}{dx}$.$\frac{dy}{dx} = \frac{1}{9} x^{-2/3} = \frac{1}{9x^{2/3}}$Thus, the correct option is $A$.

The differential equation of $3y = \sqrt[3]{x} + c$ is

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